\newproblem{lay:2_3_15}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 2.3.15}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Ana Peña gil, Jan. 19th 2014} \\}{}

  % Problem statement
	Is it possible for a 4x4 matrix to be invertible when its columns do not span $\mathbb{R}^4$? Why or why not? \\
}{
  % Solution
	This is not possible.  If an 4x4 matrix does not span $\mathbb{R}^4$, then it means that their columns are not linearly independent. If the columns are linearly dependent, the determinant of the matrix is 0, so the matrix cannot be invertible. \\
}
\useproblem{lay:2_3_15}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
